Genus 2 function fields with degree 2 elliptic subfields., by Tony Shaska
We study genus 2 function fields with elliptic subfields of degree
2. The locus $\L_2$ of these fields is a 2-dimensional subvariety of
the moduli space $\mathcal M_2$ of genus 2 fields.
An equation for $\L_2$ is already in the work of Clebsch and Bolza. We
use a birational parametrization of $\L_2$ by affine 2-space
to study the relation between the j-invariants of the degree 2 elliptic
subfields. This extends work of Geyer, Lange, Stichtenoth and others.
We find a 1-dimensional family of genus 2 curves having exactly two
isomorphic elliptic subfields of degree 2; this family is parametrized by the
j-invariant of these subfields.
Tony Shaska <email@example.com>